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June 9th, 2015, 08:39 AM  #1 
Newbie Joined: May 2015 From: Portland, OR. USA Posts: 8 Thanks: 0  Expected Value
Here are two Expected Value problems. Can somebody please check my answers? 1. In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, ..., 34, 35, and 36, marked on equally spaced slots. If a player bets \$1 on a number and wins, then the player keeps the dollar and receives an additional \$35. Otherwise, the dollar is lost. 36 * (1/38) + 1 * (37/38) ≈ .03 (The book says .05. I don't understand what I did wrong) 2. A charity organization is selling \$5 raffle tickets as part of a fundraising program. The first prize is a trip to Mexico valued at \$3450, and the second prize is a weekend spa package valued at \$750. The remaining 20 prizes are \$25 gas cards. The number of tickets sold is 6000. 3450 * (1/6000) + 750 * (1/6000) + 25 * (20/6000) + /5 (5987/6000) ≈ 4.2 Last edited by greg1313; June 10th, 2015 at 12:30 PM. 
June 10th, 2015, 12:20 PM  #2  
Senior Member Joined: Feb 2010 Posts: 702 Thanks: 137  Quote:
$\displaystyle 35 \cdot \frac{1}{38} + (1) \cdot \frac{37}{38} = \frac{2}{38}$. You don't actually win $\displaystyle \$36$. You bet $\displaystyle \$1$. That dollar is yours until you lose. If you win, you get that dollar back making everything even. Then you get your winnings of $\displaystyle \$35$. Last edited by greg1313; June 10th, 2015 at 12:31 PM.  
June 10th, 2015, 02:14 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,682 Thanks: 658 
What is the question for 2? Also what is"+ /5 (5987/6000)"?

June 10th, 2015, 03:35 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
I suspect that was supposed to be "5" rather than "/5".

June 11th, 2015, 06:20 AM  #5 
Newbie Joined: May 2015 From: Portland, OR. USA Posts: 8 Thanks: 0  
June 11th, 2015, 06:33 AM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
Method #2: You win \$35 if you hit the number and lose \$1 otherwise. Expected value is 35 * 1/38 + 1 * 37/38 = 0.0526.... You can see that you combined parts from these two correct methods to get an incorrect method. :( Quote:
 

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